Photo App on MacBook Pro unbearably slow

Yes - ExFAT doesn't support the data structures needed by a photos library. Apart from anything else, you are likely to be building up damage in your library over time. Eventually there is a risk that it will stop working altogether.

I would strongly suggest not using it further until you are able to transfer to a correctly formatted drive. After that, it might be worth trying a repair process on it. (Don't try to repair on the ExFAT drive - that could make things worse). I'd also suggest having a backup of the library before attempting a repair - even on a correctly formatted drive.

Hi

Is the external drive correctly set up for using with a photos library?

It must be formatted APFS or MacOS extended (journaled) (preferred for spinning drives)

It Must not be (or have been) used for time machine.

It must have the 'ignore ownership" checkbox ticked.

It should not be on a memory stick, SD or similar.

It must also not be a network drive (a direct connection is required - eg USB or Thunderbolt).

File sharing services such as iCloud Drive, Drop box, Onedrive etc are not compatible with Photos libraries.

See

https://support.apple.com/en-gb/HT201517

As to the problem with the Recently Deleted album you cannot empty.

You should not let the Recently Deleted album get very full. Photos may hang when trying to empty a ver full recently Deleted album, and it is not safe to have a full album, because you will not be able to see, if you accidentally moved a photo to Recently Deleted that you need to keep. When you are deleting large batches of Photos, do it in smaller groups, not more than a few hundred at a time.

Once you have moved your library to a correctly formatted external volume, and have repaired it (Repair your library in Photos on Mac - Apple Support), I would take out the items, that are currently in Recently Deleted. Put them back into an album, where you can find them all together. Then move them back to Recently Deleted, but not all at once, and then empty Recently Deleted for each batch of photos you put there.